Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | Aut(G) order 8872848 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5358 |
| direct product | C2×D2679 |
| unambiguous semidirect product | (C2×C3)⋊D893 |
| unambiguous semidirect product | (C2×C19)⋊D141 |
| unambiguous semidirect product | (C2×C47)⋊D57 |
| Fitting, socle | C2×C3×C19×C47 ⋊ C2 |
| derived, Hall | C3×C19×C47 ⋊ C22 |
| Hall | C19×C47 ⋊ C2×D3 |
| Hall | C3×C47 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D57 |
| Sylow | C19 ⋊ C2×D141 |
| Sylow | C3 ⋊ C2×D893 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2679 |
| commutator, cosocle, hypocenter | C3×C19×C47 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C19×C47 | C2 |
| LCS | G ▷ C3×C19×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D8037, C2×C3⋊(C47⋊(D19⋊C3)), D3×D2679, … |
| maximal normal subgroup of | C2×C3⋊(C47⋊(D19⋊C3)), C2×C3×D2679, D10716 |
| maximal quotient of | C2×D8037, D3×D2679, C2×C3×D2679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 28);